Question: The equation of a circle $C$ is $x^2+y^2+2x+4y+1 = 0$. What is its center $(h, k)$ and its radius $r$ ?
To find the equation in standard form, complete the square. $(x^2+2x) + (y^2+4y) = -1$ $(x^2+2x+1) + (y^2+4y+4) = -1 + 1 + 4$ $(x+1)^{2} + (y+2)^{2} = 4 = 2^2$ Thus, $(h, k) = (-1, -2)$ and $r = 2$.